Summary
A matrix converter (MC) is a topology for ac‐ac power conversion that has been widely investigated and compared with conventional ac‐dc‐ac topologies because of its attractive features. The MC is formed of controlled active devices and does not include any sizeable passive components. The converter can be used to directly control single/three/multiphase loads. MCs are highly effective in controlling the power factor and providing sinusoidal input and output currents. This paper provides a comprehensive state of the art review of the MC and discusses the main topology variations including single‐phase conventional and isolated MCs, three‐phase direct and indirect MCs, impedance source (Z‐source) MCs, multiphase MCs, and multilevel MCs (MMCs). The aim of this research article is to provide a one‐stop information on single/three/multiphase matrix, Z‐source matrix, and multilevel MCs for potential readers, researchers, and practicing engineers.